consider a situation where $p(a)=\frac{4}{5}$ and $p(a \text{ and } b)=\frac{1}{2}$. if the events are…

consider a situation where $p(a)=\frac{4}{5}$ and $p(a \text{ and } b)=\frac{1}{2}$. if the events are independent, then what is $p(b)$?\n$\frac{3}{10}$\n$\frac{1}{2}$\n$\frac{5}{8}$\n$\frac{4}{5}$

consider a situation where $p(a)=\frac{4}{5}$ and $p(a \text{ and } b)=\frac{1}{2}$. if the events are independent, then what is $p(b)$?\n$\frac{3}{10}$\n$\frac{1}{2}$\n$\frac{5}{8}$\n$\frac{4}{5}$

Answer

Answer:

C. $\frac{5}{8}$

Explanation:

Step1: Recall the formula for independent events

For independent events $A$ and $B$, $P(A\cap B)=P(A)\times P(B)$.

Step2: Rearrange the formula to solve for $P(B)$

$P(B)=\frac{P(A\cap B)}{P(A)}$.

Step3: Substitute the given values

Given $P(A)=\frac{4}{5}$ and $P(A\cap B)=\frac{1}{2}$, then $P(B)=\frac{\frac{1}{2}}{\frac{4}{5}}$.

Step4: Simplify the fraction

$P(B)=\frac{1}{2}\times\frac{5}{4}=\frac{5}{8}$.